# Mathematics

## Instructions

 Instructions: Week 5 Individual Assignment Total Number of Questions – 12 Total Points: 6 1. You have twelve problems – on each tab of this Excel file. 2. Please show your work in the cells. Use Excel formulas instead of writing the values/answers directly in the cell. The instructor will then know where you made a mistake and provide you valuable feedback and partial credit (if appropriate).

## Question 1

 Find the interest paid on a loan of \$1,200 for three years at a simple interest rate of 5% per year. How much money will you pay after three years? Principal Rate Time Simple Interest (SI) Maturity Value

## Question 2

 Find the maturity value of a loan of \$1,750 for 28 months at 9.8% simple interest per year. Principal Rate Time — Please make sure that the time periods for Time and Rate match. Simple Interest (SI) Maturity Value

## Question 3

 Find the simple interest rate of a loan of \$5,000 that is made for three years and requires \$1,762.50 in interest. Principal Time SI Rate

## Question 4

 A loan of \$16,840 is borrowed at 9% simple interest and is repaid with \$4,167.90 interest. What is the duration of the loan? Principal Rate SI Time

## Question 5

 How much money is borrowed if the interest rate is 9.25% simple interest and the loan is made for 3.5 years and has \$904.88 interest? SI Rate Time Principal

## Question 6

 Find the ordinary and exact interest for a loan of \$1000 at a 5% annual interest rate. The loan was made on March 15 and is due May 15. Loan date Loan date Loan Due Date Loan Due Date Exact time days Exact time days Principal Principal Rate Rate Time Time Ordinary Simple Interest (SI) Exact Simple Interest (SI)

## Question 7

 Find the bank discount and proceeds using ordinary interest for a loan to Michelle Anders for \$7,200 at 8.25% annual simple interest from August 8 to November 8. Loan date Loan Due Date Exact time days Face Value (F) Discount Rate (D) Time Period (T) years –> ‘Convert Exact time in days to years Bank Discount (B) Proceeds (P)

## Question 8

 What is the effective interest rate of a simple discount note for \$8,000, at an ordinary bank discount rate of 11%, for 120 days? Face Value (F) Discount Rate (D) Time Period (T) years –> ‘Convert Exact time in days to years Bank Discount (B) Proceeds (P) Rate

## Question 9

 SOLVED EXAMPLE What is the effective interest rate for the ﬁrst year for a loan of \$20,000 for three years if the interest is compounded quarterly at a rate of 12%? Quoted Rate 12.00% quarterly No. of compounding periods per year 4 For Quarterly, type 4; for semiannually, type 2; for annually, type 1; for monthly, type 12; for daily, type 365 EAR 12.55% 1. Ross Land has a loan of \$8,500 compounded quarterly for four years at 6%. What is the effective interest rate for the ﬁrst year for the loan? Quoted Rate No. of compounding periods per year For Quarterly, type 4; for semiannually, type 2; for annually, type 1; for monthly, type 12; for daily, type 365 EAR 2. Find the effective interest rate for the ﬁrst year for a loan for four years compounded semiannually at an annual rate of 2% Quoted Rate No. of compounding periods per year For Quarterly, type 4; for semiannually, type 2; for annually, type 1; for monthly, type 12; for daily, type 365 EAR 3. What is the effective interest rate for the ﬁrst year for a loan of \$5,000 at 10% compounded daily for three years? Quoted Rate No. of compounding periods per year For Quarterly, type 4; for semiannually, type 2; for annually, type 1; for monthly, type 12; for daily, type 365 EAR 4. Depending on the issuer, a typical credit card agreement quotes an interest rate of 18 percent APR. Monthly payments are required. What is the actual interest rate you pay on such a credit card? Quoted Rate No. of compounding periods per year For Quarterly, type 4; for semiannually, type 2; for annually, type 1; for monthly, type 12; for daily, type 365 EAR =EFFECT(B30, B31) 5. Find the effective interest rate for a loan of \$3,500 at 10% interest compounded quarterly. Quoted Rate No. of compounding periods per year For Quarterly, type 4; for semiannually, type 2; for annually, type 1; for monthly, type 12; for daily, type 365 EAR =EFFECT(B36, B37)

## Question 10

 SOLVED EXAMPLE Tim Bowling has \$20,000 invested for three years at a 5.25% annual rate compounded daily. How much interest will he earn? Initial Investment (PV) \$20,000 Quoted Rate 5.25% Compounding Frequency Daily Choose one Number of compoundings (m) 365 For Quarterly, type 4; for semiannually, type 2; for annually, type 1; for monthly, type 12; for daily, type 365 Quoted Rate divided by m = RATE 0.0144% Number of Years 3 NPER (Num. of years * m) 1095 Ending Amount (FV) \$23,411.35 Compound Interest \$3,411.35 Exercise Find the future value of a \$15,000 money market investment at 2.8% annual interest compounded daily for three years. Initial Investment (PV) Quoted Rate Compounding Frequency Number of compoundings (m) Quoted Rate divided by m = RATE Number of Years NPER (Num. of years * m) Ending Amount (FV) Compound Interest

## Question 11

 SOLVED EXAMPLE The Holiday Boutique would like to put away some of the holiday profits to save for a planned expansion. A total of \$8,000 is needed in three years. How much money in a 5.2% three-year certificate of deposit that is compounded monthly must be invested now to have the \$8,000 in three years? Future Value Needed (FV) \$8,000 Quoted Rate 5.2% Compounding Frequency Monthly Choose one Number of compoundings (m) 12 For Quarterly, type 4; for semiannually, type 2; for annually, type 1; for monthly, type 12; for daily, type 365 Quoted Rate divided by m = RATE 0.4333% Number of Years 3 NPER (Num. of years * m) 36 Amount Invested Now (PV) \$6,846.78 Exercise How much should be invested now to have \$15,000 in six years if interest is 4% compounded quarterly? Future Value Needed (FV) Quoted Rate Compounding Frequency Number of compoundings (m) Quoted Rate divided by m = RATE Number of Years NPER (Num. of years * m) Amount Invested Now (PV)

## Question 12

 Jamie Juarez needs \$12,000 in 10 years for her daughter’s college education. How much must be invested today at 2% annual interest compounded semiannually to have the needed funds? Future Value Needed (FV) Quoted Rate Compounding Frequency Choose one Number of compoundings (m) For Quarterly, type 4; for semiannually, type 2; for annually, type 1; for monthly, type 12; for daily, type 365 Quoted Rate divided by m = RATE Number of Years NPER (Num. of years * m) Amount Invested Now (PV) A loan of \$8,000 for two acres of woodland is compounded quarterly at an annual rate of 6% for ﬁve years. Find the compound amount and the compound interest. Initial Investment (PV) Quoted Rate Compounding Frequency Choose one Number of compoundings (m) For Quarterly, type 4; for semiannually, type 2; for annually, type 1; for monthly, type 12; for daily, type 365 Quoted Rate divided by m = RATE Number of Years NPER (Num. of years * m) Ending Amount (FV) Compound Interest

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